Unified geometric theory of gravity and supergravity
TL;DR: In this article, a unified geometric formulation of gravitation and supergravity is presented, which is constructed out of the components of the curvature tensor for bundle spaces with four-dimensional Lorentz base manifold and structure groups Sp(4) for gravity and OSp(1, 4) for supergravity.
Abstract: A unified geometric formulation of gravitation and supergravity is presented. The action for these theories is constructed out of the components of the curvature tensor for bundle spaces with four-dimensional Lorentz base manifold and structure groups Sp(4) for gravity and OSp(1,4) for supergravity. The requirement of invariance under reflections, local Lorentz transformations, and general coordinate transformations uniquely determines the action and ensures the existence of local supersymmetry in supergravity.
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TL;DR: By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels.
2,636 citations
TL;DR: In this article, the action and transformation laws of supergravity in 11 dimensions were presented, which is expected to be closely related to the O(8) theory in 4 dimensions after dimensional reduction.
1,654 citations
TL;DR: In this article, the authors present explicit models for a symmetry breakdown in the cases of the Weyl (or homothetic) group, the SL(4, R), or the GL(4-R) covering subgroup.
1,474 citations
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TL;DR: In this paper, a review of recent progress in massive gravity is presented, showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali-Gabadadze-Porrati model, cascading gravity and ghost-free massive gravity.
Abstract: We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali-Gabadadze-Porrati model, cascading gravity and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware-Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally we present alternative and related models of massive gravity such as new massive gravity, Lorentz-violating massive gravity and non-local massive gravity.
924 citations
TL;DR: In this paper, the present status of the spin-foam approach to the quantization of gravity is reviewed and a pedagogical presentation of new models for four-dimensional quantum gravity is paided to the recently introduced new models.
Abstract: This article reviews the present status of the spin-foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently-introduced new models for four-dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.
629 citations